Final answer:
The approximate altitude for an artificial satellite with a 90-minute orbit is around 200-400 km, which is typical of Low Earth Orbits (LEO). None of the provided options align with this realistic altitude, as they all represent higher orbits.
Step-by-step explanation:
To determine the approximate altitude of an artificial satellite that completes one orbit around the Earth in 90 minutes, we can invoke Kepler's Third Law, which states that the square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit. This law applies to any orbiting body, including satellites. However, for this level of an estimation, we look at common orbits for satellites, as Kepler's Law calculations would require more complex computations.
The options provided suggest discrete orbits, where each corresponds to a particular type of orbit. An orbital period of 90 minutes is characteristic of a Low Earth Orbit (LEO). For instance, the International Space Station (ISS) orbits Earth approximately every 90 minutes and is located about 400 km above Earth. Thus, we can eliminate options (a) 26,000 km, (b) 35,786 km (geostationary orbit), (c) 42,164 km, and (d) 63,781 km as they are too high for a 90-minute orbit.
Considering the proximity of the ISS orbit to the Earth and its period, an altitude much lower than those listed would be expected for a 90-minute orbit. The altitudes given in the options are not typical for such a short period, so this question seems to have some inconsistencies with the reality of satellite orbits. A satellite with a 90-minute orbit will generally have an altitude of approximately 200-400 km above Earth's surface, none of the options provided match a realistic altitude for a 90-minute orbiting satellite.